Results 161 to 170 of about 13,435 (197)
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2016
The Gauss–Bonnet theorem is the most famous result in the study of surfaces. It provides a satisfying final chapter of this textbook because it interrelates many fundamental concepts from the previous five chapters.
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The Gauss–Bonnet theorem is the most famous result in the study of surfaces. It provides a satisfying final chapter of this textbook because it interrelates many fundamental concepts from the previous five chapters.
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2010
The Gauss–Bonnet theorem is the most beautiful and profound result in the theory of surfaces. Its most important version relates the average of the Gaussian curvature to a property of the surface called its ‘Euler number’ which is ‘topological’, i.e., it is unchanged by any diffeomorphism of the surface.
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The Gauss–Bonnet theorem is the most beautiful and profound result in the theory of surfaces. Its most important version relates the average of the Gaussian curvature to a property of the surface called its ‘Euler number’ which is ‘topological’, i.e., it is unchanged by any diffeomorphism of the surface.
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Stochastic Local Gauss-Bonnet-Chern Theorem
Journal of Theoretical Probability, 1997The Gauss-Bonnet-Chern theorem is the index theorem for the Hodge-de Rham Laplacian on differential forms. This theorem for a compact Riemannian manifold (without boundary) is discussed to exhibit in a clear manner the role that Riemannian Brownian motion plays in various probabilistic approaches to index theorems.
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2019
It must have been studied in the subject of line integration in calculus that the integration of a differential 1-form.
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It must have been studied in the subject of line integration in calculus that the integration of a differential 1-form.
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1997
The idea of Chern is brilliantly simple: it is best to present the words of the master himself:
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The idea of Chern is brilliantly simple: it is best to present the words of the master himself:
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1979
In this chapter we shall study the integral ∫ s K of the Gaussian curvature over a compact oriented 2-surface S. We shall see that (1/2π) ∫ s K always turns out to be an integer, the Euler characteristic of S. This is the 2-dimensional version of the Gauss-Bonnet theorem.
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In this chapter we shall study the integral ∫ s K of the Gaussian curvature over a compact oriented 2-surface S. We shall see that (1/2π) ∫ s K always turns out to be an integer, the Euler characteristic of S. This is the 2-dimensional version of the Gauss-Bonnet theorem.
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Gauss–Bonnet's Theorem and Closed Frenet Frames
Geometriae Dedicata, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Gauss-Bonnet theorem and ?(2)
Geometriae Dedicata, 1984Using a counting argument in hyperbolic geometry due to Siegel and the Gauss-Bonnet theorem, we compute that ζ(2)=π2/6.
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The Generalized Gauss-Bonnet Theorem
2004In this chapter we shall prove the Generalized Gauss-Bonnet Theorem using tubes. The principal ingredients are: (1) H. Hopf’s generalization [Hopfl], [Hopf2] of the Gauss-Bonnet Theorem for hypersurfaces in ℝn, (2) the Nash Embedding Theorem [Nash], (3) Weyl’s Tube Formula [Weyll], and (4) some elementary calculations with volumes of tubes and Euler ...
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